injection at different conditions and scales Odd Andersen and Halvor - PowerPoint PPT Presentation

Simplified models for thermal effects of CO 2 injection at different conditions and scales Odd Andersen and Halvor Møll Nilsen, SINTEF Digital, Norway TCCS, 14th June 2017

Motivation ◮ Thermal effects from injection will affect: ◮ fluid flow ◮ geomechanics ◮ geochemistry ◮ Fully resolved, fully coupled models are expensive. ◮ Can we model the thermal field using simplified models? ◮ Are vertical equilibrium models adequate when modeling the heat front ◮ To what extent does the overburden need to be taken into account 2 / 22

Conceptual model overburden mean pos. tip (convection only) inner pos. thermal CO 2 plume front bleed aquifer Q (advection and convection) underburden thermal front tip (convection only) mean pos. inner pos. r 3 / 22

Flow models 3D grid Full 3D ◮ CO 2 saturation ◮ pressure ◮ temperature → One value per cell r Vertical Equilibrium 1 ◮ plume thickness ◮ caprock pressure VE grid ◮ temperature → One value per vertical pillar Vertical Equilibrium 2 → as above, but two temperature r values per vertical pillar (CO 2 and brine) 4 / 22

Overburden models 2 L ′ c High vertical resolution r Low vertical resolution r Adiabatic (ignore bleed) r c = 2 √ t end D ′ (“bleeding length scale”) L ′ 5 / 22

Heat flow and grid resolution ◮ We compare with the continuous case of 1D heat diffusion: ◮ ∂ t T − ∂ z ( D∂ z T ) = 0 for z ∈ [0 , inf] ◮ T ( z, 0) = T 0 ∀ z ∈ [0 , ∞ ) ◮ T (0 , t ) = T 1 ∀ t ∈ (0 , t end ] ◮ → Solution: T ( z, t ) = T 0 + ( T 1 − T 0 ) erfc ( z/L c ) � ◮ Heat leaked by time t then equals 2( T 1 − T 0 ) Dt π ◮ Finite-volume solution if domain consists of single gridcell of length 2 L c : t � � ◮ T ( t ) = T 0 + ( T 1 − T 0 ) 1 − e − 8 t end � t � ◮ Heat leaked by time t then equals 2 L c ( T 1 − T 0 ) 1 − e − 8 t end ◮ At t = t end ◮ Heat leaked (analytic): ( T 1 − T 0 ) 1 √ π L c ≈ 0 . 56( T 1 − T 0 ) L c ◮ Heat leaked (single-cell): � 1 − e − 1 � 2 L c ( T 1 − T 0 ) ≈ 0 . 24( T 1 − T 0 ) L c 8 ◮ For t < t end , heat leakage for single-cell case is approximately linear in time. 6 / 22

Numbers describing the system Where: ◮ D = λ eff aq / ( ρc ) eff aq Q inj R ◮ Peclet number: P e = ◮ D ′ = λ ob / ( ρc ) ob 4 πφHD √ ( ρc ) co 2 ◮ Bleed: Bl = h ′ ◮ R = φ tD ′ ( ρc ) eff H aq ◮ Gravity number: Γ = 2 πk ∆ ρgH 2 ◮ h ′ = ( ρc ) ob ( ρc ) eff µ w Q inj aq ◮ ∆ ρ = ρ w − ρ co 2 Parameter ranges: Parameter symbol unit min. value max. value Porosity φ 0.15 0.4 Permeability k darcy 0.013 2 Aq. thickness m 10 200 H Aq. thermal conductivity λ aq W/(m K) 1.2 6.4 Ob. thermal conductivity W/(m K) 1.2 6.4 λ ob kg/m 3 Aq. rock density ρ aq 2500 2800 Ob. rock density kg/m 3 2500 2800 ρ ob Aq. heat capacity c aq J/(kg K) 640 900 Ob. heat capacity J/(kg K) 640 900 c ob Aquifer depth d m 1000 3000 Thermal gradient K/km 25 50 ∇ T Injection temp. T inj K 5 + 273.15 50 + 273.15 Injection rate kg/s 0.1 MT 20 MT ρ CO 2 Q inj 7 / 22

Ranges for P e , Γ and Bl Γ ∈ [3 . 5 × 10 − 3 , 4 . 2 × 10 3 ] P e ∈ [3 . 7 × 10 − 1 , 1 . 4 × 10 4 ] √ t ∈ [3 . 0 × 10 − 6 , 2 . 5 × 10 − 4 ] Bl/ ◮ These extremal values are not independent of each other, and cannot all be reached at the same time! ◮ We eliminate parameter combinations that lead to excess pressure buildup. 8 / 22

High Peclet ( 1 . 4 × 10 4 ), High Bleed ( 2 . 3 × 10 − 4 √ t ) 9 / 22

High Peclet ( 1 . 4 × 10 4 ), Low Bleed ( 6 . 0 × 10 − 5 √ t ) 10 / 22

Low Peclet ( 3 . 7 × 10 − 1 ), High Bleed ( 1 . 2 × 10 − 5 √ t ) 11 / 22

Low Peclet ( 3 . 7 × 10 − 1 ), Low Bleed ( 3 . 0 × 10 − 6 √ t ) 12 / 22

High Bleed ( 2 . 4 × 10 − 4 √ t ), High Peclet ( 8 . 0 × 10 3 ) 13 / 22

High Bleed ( 2 . 4 × 10 − 4 √ t ), Low Peclet ( 1 . 5 × 10 3 ) 14 / 22

Low Bleed ( 3 . 0 × 10 − 6 √ t ), High Peclet ( 1 . 3 × 10 3 ) 15 / 22

Low Bleed ( 3 . 0 × 10 − 6 √ t ), Low Peclet ( 2 . 4 × 10 2 ) 16 / 22

High Γ ( 4 . 1 × 10 3 ), High Pe ( 2 . 0 ), High Bl ( 1 . 2 × 10 − 5 √ t ) 17 / 22

High Γ ( 4 . 1 × 10 3 ), High Pe ( 2 . 0 ), Low Bl ( 3 . 0 × 10 − 6 √ t ) 18 / 22

Result summary 19 / 22

Result summary: high Γ 20 / 22

Tentative conclusions ◮ Plume shape always remain unaffected by heat model (but VE is not always able to represent it correctly) ◮ Pressure ok in most scenarios, but worse for the low Pe cases, which also have low gravity numbers ◮ Shape is generally captured by the low-resolution overburden model, but front position is significantly affected. ◮ The adiabatic model usually gives wildly wrong front position, but approximately OK for low Peclet and Bleed numbers. ◮ Higher gravity numbers yield worse results for VE models ◮ A VE model able to represent thermal front shapes in the general case would need more than two values per column. 21 / 22

Acknowledgments The work presented here was carried out with support from the Norwegian Research Council, project 243729. 22 / 22